Make the equation of the circle whose diameter is the segment AB if A (-4; 7) B (6; -3)

1. Find the coordinates of the center of the circle, which is in the middle of the diameter AB:

A (-4; 7);
B (6; -3);
x0 = (-4 + 6) / 2 = 2/2 = 1;
y0 = (7 – 3) / 2 = 4/2 = 2;
O (x0; y0) = O (1; 2).

2. Calculate the radius of the circle:

R = 1/2 * AB = 1/2 * √ ((6 + 4) ^ 2 + (-3 – 7) ^ 2) = 1/2 * √ (10 ^ 2 + 10 ^ 2) = 1/2 * √200 = 1/2 * 10 * √2 = 5√2.

3. Equation of a circle with center at point O (x0; y0) and radius R:

(x – x0) ^ 2 + (y – y0) ^ 2 = R ^ 2;
(x – 1) ^ 2 + (y – 2) ^ 2 = (5√2) ^ 2;
(x – 1) ^ 2 + (y – 2) ^ 2 = 50.
Answer: (x – 1) ^ 2 + (y – 2) ^ 2 = 50.